Bibliografia

[A-M] R. Abraham, J. Marsden Foundations of Mechanics, Addison–Wesley, New York,

1985.

[Ah] K.S. Ahluwalia Fundamentals of Poisson Lie Groups with Applications to the Clas-

sical Double, pre-pubblicazione DAMTP 93-53, hep-th/9310068, 1994. [Al-M] A. Yu. Alekseev, A.Z. Malkin Symplectic structures associated to Poisson–Lie

groups, Comm. Math. Phys. 162 (1994), 147–173.

[A1] V.I. Arnold Small denominators III. Small denominators and problems of stability of motion in classical and celestial mechanics, Russ. Math. Surveys 18 (1963), 85–191.

[A2] V.I. Arnold Mathematical methods of classical mechanics, GTM 60, Springer, New York–Berlin, 1989^{2} (trad. dal russo).

[Au] M. Audin (ed.) Holomorphic curves in Symplectic Geometry, Progr. Math. 118, Birkhäuser, Basel, 1994.

[Be] F.A. Berezin Some remarks about the associated envelope of a Lie algebra, Funct. Anal. Appl. 1 (1967), 91–102.

[B-R] K.H. Bhaskara, K. Rhama Quadratic Poisson structures, J. Math. Phys. 32 (1991),

2319–2322. [B-V1] K.H. Bhaskara, K. Viswanath, Calculus on Poisson manifolds, Bull. London Math.

Soc. 20(1988), 68–72. [B-V2] K.H. Bhaskara, K. Viswanath, Poisson algebras and Poisson manifolds, Pitman

Res. Notes in Math. 174, Longman, New-York, 1988.

[Bi] L. Bianchi Lezioni sulla teoria dei gruppi continui finiti di trasformazioni, E. Spoerri, Pisa, 1903.

[Bk] R. Bkouche Idéaux mous d’un anneau commutatif. Applications aux anneaux de fonctions, C. R. Acad. Sci. Paris 260 (1965), 6496–6498.

[Br] J.-L. Brylinski A differential complex for Poisson manifolds, J. Differential Geom-

etry 28 (1988), 93–114.

[C-G-O-P] M. Cahen, S. Gutt, C. Ohn, M. Parker Lie–Poisson groups: remarks and examples,

Lett. in Math. Phys. 19 (1990), 343–353.

[C-G-R1] M. Cahen, S. Gutt, J. Rawnsley Nonlinearizability of the Iwasawa Poisson struc-

ture, Lett. Math. Phys. 24 (1992), 79–83.

[C-G-R2] M. Cahen, S. Gutt, J. Rawnsley Some Remarks on the Classification of Poisson

Lie Groups,??? AMS, 1994, 1–16. [C-W] A. Cannas da Silva, A. Weinstein Geometric Models for Noncommutative Algebras,

Berkeley, 1998 (pre-pubblicazione da richiedere agli autori).

[Ca] H. Cartan Notions d’algébre differentielle, Coll. de Top. Bruxelles (1950), 15–27. [C-E] H. Cartan, S. Eilenberg Homological Algebra, Princeton, 1956. [C-M] P.R. Chernoff, J.E. Marsden Properties of Infinite Dimensional Hamiltonian Sys-

tems, Lect. notes in Math. 425, Springer, New York–Berlin, 1974.

[Cn1] J. Conn Normal forms for analytic Poisson structures, Ann. of Math. 119 (1984), 576–601.

[Cn2] J. Conn Normal forms for smooth Poisson structures, Ann. of Math. 121 (1985), 565–593.

[Co1] A. Connes The von Neumann algebra of a foliation, in in Lect. Notes in Phys. 80, Springer, 1978.

[Co2] A. Connes Sur la théorie non commutative de l’intégration, in Lect. Notes in Math. 725, Springer, 1979.

[Co3] A. Connes A survey of foliations and operator algebras, in Proc. Symposia in Pure Math. R.V. Kadison (ed.), AMS, Providence, 1982.

[Co4] A. Connes Non-Commutative Geometry, Academic Press, New York, 1994.

[Cr] T. Courant Dirac manifolds, Trans. Amer. Math. Soc. 319 (1990), 631–661. [Cr-W] T. Courant, A. Weinstein Beyond Poisson manifolds, Seminaire sur-rhodanien de

géométrie VIII. Travaux en Cours 27, Hermann, Paris (1988). [D-W] P. Dazord, A. Weinstein (Ed.) Symplectic Geometry, Grupoids and Integrable

Systems, Séminaire Sud-Rhodanien de Géométrie à Berkeley (1989), MSRI Series, Springer, Berlin–New York, 1991.

[Dd] J. Dieudonné Elements d’analyse, III, Gauthier–Villars, Paris, 1970.

[D1] P.A.M. Dirac Generalized Hamiltonian Dynamics, Can. J. Math. 2 (1950), 129– 148.

[D2] P.A.M. Dirac Lectures on Quantum Mechanics, Belfer Monograph Series 2, Yeshiva Univ., New York, 1964.

[Di] J. Dixmier Les algebres des operateurs dans les espaces hilbertiennes, Gauthiers-

Villars, Paris, 1957. [D-G] I.Ya. Dorfman, I.M. Gel’fand Hamiltonian Operators and Algebraic Structures re-

lated to them, Funct. Anal. Appl. 13 (1979), 248–262.

[Dr] V.G. Drinfeld Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang–Baxter equation, Soviet Math. Doklady 27 (1983), 68–71.

[Du] J. P. Dufour Linéarisation de certaines structures de Poisson, J. Differential Geometry 32 (1990), 415–428.

[D-H] J.P. Dufour, A. Haraki Rotationelles et structures de Poisson quadratiques, C. R. A-

cad. Sci. Paris Série I, Math. 312 (1991), 137–140. [F-L] D.R. Farkas, G. Letzter Ring theory from symplectic geometry, J. Pure Appl. Alg.

125 (1998), 155-190.

[Fe] B. Fedosov Deformation Quantization and Index Theory, Akademie Verlag, Berlin, 1996.

[Fu] J. Fuchs Affine Lie algebras and quantum groups, Cambridge U.P., 1992.

[Fk] D.B. Fuks Cohomology of infinite dimensional Lie algebras, Consultants Bureau, New York, 1986 (trad. dal russo).

[Gi] V. Ginzburg Momentum mappings and Poisson cohomology, Intern. Journal of

Math. 7 (1996), 329–358. [G-W] V. Ginzburg, A. Weinsten Lie–Poisson structure on some Poisson–Lie groups,

Journal A.M.S. 5 (1992), 445–453.

[Hu] J. Huebschmann Poisson cohomology and quantization, J. Reine Angew. Math. 408 (1990), 57–113.

[Hm] J.E. Humphreys Introduction to Lie Algebras and Representation Theory, GTM 9, Springer, New York–Berlin, 1972.

[Ja] Jacobi Vorlesungen über Dynamik, Reimer Verlag, 1864.

[Jo] R. Jost Poisson brackets (an unpedagogical lecture), Rev. Mod. Phys. 36 (1964),

572–579. [K-R] R. Kadison, Ringrose Fundamentals of the Theory of Operator Algebras, II , Aca-

demic Press, Orlando, 1986. [K-M] M.V. Karasaev, V.P. Maslov Nonlinear Poisson Brackets. Geometry and Quan-

tization., Transl. of Math. Monographs 119, A.M.S., Providence, 1993 (trad. dal russo).

[Ki1] A.A. Kirillov Unitary representations of nilpotent Lie groups, Russ. Math. Surveys 17 (1962), 53–104.

[Ki2] A.A. Kirillov Elements of the Theory of Representations, Springer, New York– Berlin, 1976.

[Ki3] A.A. Kirillov Local Lie algebras, Russ. Math. Surveys 31 (1976), 55–75. [K-N] S. Kobayashi, K. Nomizu Foundations of Differential Geometry, Wiley, New York,

1963.

[Kv] M. Konsevitch Deformation quantization of Poisson Manifolds, I , pre-pubblica-

zione q-alg/9709040, 1997.

[Kn] B. Konstant Quantization and Unitary Representations, Lect. Notes in Math. 570, Springer, New York–Berlin, 1970, 177–306.

[KS] Y. Kosmann-Schwartzbach Lie bialgebras, Poisson Lie groups and dressing transformations, Lect. Notes in Phys. 495, Springer, New York–Berlin, 1997.

[Ko] J.L. Koszul Crochet de Schouten–Nijenhuis et cohomologie, Astérisque (hors série), Soc. Math. de France, 1985, 257–271.

[Kr] I.S.Krasil’ščikh Hamiltonian cohomology of canonical algebras, Soviet. Math. Dokl. 21

(1980) 625–629. [K-L-V] I.S.Krasil’ščikh, V.V. Lychagin, A.M. Vinogradov Geometry of Jet Spaces and

Nonlinear Partial Differential Equations, Adv. Stud. in Contemp. Math. 1, Gordon&Breach, New York, 1986.

[K-V] I.S.Krasil’ščikh, A.M. Vinogradov What is the Hamiltonian Formalism?, Russian

Math. Surveys 30 (1975), 177–202.

[La] J.-L. Lagrange Mécanique Analytique, Chez la Veuve Desaint, Paris, 1811^{2}. [L-L] L.D. Landau, E.M. Lifchitz Physique théorique, I. Mécanique, MIR, Moscou, 1982

(trad. dal russo). [L-M] P. Libermann, Ch.M. Marle Symplectic Geometry and Anaytical Mechanics, Kluwer,

Dordrecht, 1987.

[Li] A. Lichnerowicz Les variétés de Poisson et leurs algèbres de Lie associées, J. Differential Geometry 12 (1977), 253–300.

[Lie] M.S. Lie Theorie der Transformationgruppen, II (unter Mitwirkung von F. Engel), Teubner, Leipzig, 1890^{2}.

[L-Q] Z.-J. Liu, M. Qian Generalized Yang–Baxter equations, Koszul operators and Pois-

son Lie groups, J. Differential Geometry 35 (1992), 399–414. [L-X] Z.-J. Liu, P. Xu On quadratic Poisson structures, Lett. in Math. Phys. 26 (1992)

33–42.

[Lo] J.-L. Loday Cyclic Homology, Springer, New York–Berlin, 1992 [L-R] J.-L. Lu, T. Ratiu On the nonlinear convexity theorem of Konstant, Journal

A.M.S. 4 (1991), 349–363. [L-W] J.H. Lu, A. Weinstein Poisson Lie groups, dressing transformations and Bruhat

decomposition, J. Differential Geometry 31 (1990), 501–526.

[Ma] K. Mackenzie Lie Groupoids and Lie Algebroids in Differential Geometry, London

Math. Soc. Lectures Notes Series 124, Cambridge U.P., 1987. [M-R1] J.E. Marsden, T.S. Ratiu, Reduction of Poisson manifolds, Lett. Math. Phys. 11

(1986), 161-170. [M-R2] J.E. Marsden, T.S. Ratiu, Introduction to Mechanics and Symmetry, Springer,

New York–Berlin, 1994. [M-W] J.E. Marsden, A. Weinstein Reduction of symplectic manifolds with symmetry,

Rep. Math. Phys. 5 (1974), 121–130. [Mc-S] D. McDuff, D. Salamon An introduction to symplectic topology, Oxford U.P., 1995.

[M-S] C.C. Moore, C. Schochet Global Analysis on Foliates Spaces, MSRI Publ., Springer,

New York–Berlin, 1988.

[Mo] J. Moser On the volume element of a manifold, Trans. Amer. Math. Soc. 120 (1965), 280–296.

[Ni] N. Nakanishi Poisson cohomology of Poisson quadratic structures, Publ. RIMS 33 (1997), 73–89.

[vN] J. von Neumann On rings of operators. Reduction theory, Ann. of Math. 50 (1949), 401–485.

[Ol] P.J. Olver Applications of Lie Groups to Differential Equations, GTM 107, Springer, New York–Berlin, 1986.

[Pa] W. Pauli On the Hamiltonian structure of non-local field theory, Nuovo Cimento 10 (1953), 648–667.

[Po] S.-D. Poisson Mémoire sur la variation des costantes arbitraires dans les questions de Mécanique, Journ. de l’Ecole Politecnique 8 (1809) pp.266–344.

[Pn] L.S. Pontriagin Topological Groups, Princeton, 1939 (trad. dal russo).

[Ps] M.M. Postnikov Lie groups and Lie algebras, MIR, Moscow, 1985 (trad. dal russo).

[Ri] B.L. Reinhart Differential Geometry of Foliations, Springer, Berlin–New York,

1983.

[R-V-W] N. Reshetikhin, A.A. Voronov, A. Weinstein Semiquantum geometry, Berkeley,

1996 (pre-pubblicazione da richiedere agli autori). [R-S] A.G. Reyman, M.A. Semenov-Tian-Shansky Group-Theoretical Methods in the

Theory of Finite-Dimensional Integrable Systems, in V.I. Arnol’d, S.P. Novikov (Ed.) Dynamical Systems, VII , Encyclopedy of Mathematical Sciences 16, 116– 258, trad. dal russo.

[dR] G. de Rham Variétés différentiables, Hermann, Paris, 1955.

[Sch] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966^{3}.

[STS1] M.A. Semenov-Tian-Shansky What is a Classical R-Matrix?, Funct. Anal. Appl. 17 (1983), 259–272.

[STS2] M.A. Semenov-Tian-Shansky Dressing transformations and Poisson group actions, Publ. RIMS 21 (1985), 1237–1260.

[STS3] M.A. Semenov-Tian-Shansky Poisson groups and Dressing Transformations, J. of Soviet Math. 46 (1989), 1641–1657.

[STS4] M.A. Semenov-Tian-Shansky Poisson–Lie groups, quantum duality and the twisted

quantum double, Theor. Math. Phys. 93 (1992), 302–329.

[Se] J.-P. Serre Lie Algebras and Lie Groups, Lect. Notes in Math. 1500, Springer, New York–Berlin, 1992.

[Sn] J. Sniatycki Dirac brackets in geometric dynamics, Ann. Inst. H.Poincaré 20 (1974), 365–372.

[So] J.-M. Souriau Structure des systèmes dynamiques, Dunoud, Paris, 1970.

[Sr] N. Steenrod The topology of fibre bundles, Princeton, 1951.

[St] P. Stefan Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699–713.

[Su] H.J. Sussmann Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 170 (1973), 171–188.

[Sw] R.G. Swan Vector Bundles and Projective Modules, Trans. Amer. Math. Soc. 105 (1962), 264–277.

[Tr] F. Treves, Topological vector spaces, distributions and kernels, Academic Press, New York, 1967.

[Va] I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Progr. Math. 118, Birkhäuser, Basel, 1994.

[Vi] V.P. Viflyantsev Frobenius theorem for differential systems with singularities, Vestnik Moskow. Univ. 3 (1980), 11–14.

[W1] A. Weinstein The local structure of Poisson manifolds, J. Differential Geometry 18 (1983) 523–557.

[W2] A. Weinstein Poisson structures and Lie algebras, Astérisque (hors série), Soc. Math. de France, 1985, 421–434.

[W3] A. Weinstein Symplectic groupoids and Poisson manifolds, Bull. Amer. Math. Soc. 16 (1987), 101–104.

[W4] A. Weinstein Poisson geometry of the principal series and non-linearizable structure, J. Differential Geometry 25 (1987), 55–73.

[W5] A. Weinstein Coisotropic calculus and Poisson groupoids, J. Math. Soc. Japan 40 (1988), 705–727.

[W6] A. Weinstein Some remarks on dressing transformations, J. Fac. Sci. Univ. Tokyo, Sec. IA 35 (1988), 163–167.

[W7] A. Weinstein The modular automorphism group of a Poisson manifold, J. Geom. Phys. 23 (1997), 379–394.

[X1] P. Xu Morita equivalence of Poisson manifolds, Comm. Math. Phys. 142 (1991), 493–509.

[X2] P. Xu Poisson cohomology of regular Poisson manifolds, Ann. Inst. Fourier Grenoble 42 (1992), 967-988.

[X3] P. Xu Noncommutative Poisson algebras, Amer. J. Math. 116 (1994), 101–125.